System and method for simplified aircraft brake distance estimation

ABSTRACT

A braking system and method utilizing a simplified estimate of a distance between two locations on the earth based on spherical geometry. A braking system utilizing the aforementioned simplified estimate does not require computationally intensive calculations and is more efficient and better equipped to handle real-time generation of distance estimates for braking needs and variable conditions. In the present invention, geodesics evaluations are not used; rather, a modified Haversine formula that simplifies computations is used, including a one-time computation of the cosine of latitude coordinate.

CROSS-REFERENCES TO RELATED APPLICATIONS

This is a continuation based on U.S. Ser. No. 15/852,913, filed Dec. 22, 2017, which claims priority from U.S. Provisional Patent Application No. 62/439,799, filed Dec. 28, 2016, the contents of which are incorporated by reference herein in their entirety.

BACKGROUND

Aircraft manufacturers are incorporating new advanced braking systems that are designed to minimize the amount of time that an aircraft occupies an airport runway upon landing. Minimizing runway occupancy time improves the efficiency and safety of the runways and maximizes the use of the airport's resources. To minimize an aircraft's duration of the runway usage, the aircraft must decelerate from its touchdown speed to a safe taxiing speed in the most expeditious manner. For safety and reduced wear and tear on the aircraft, it is important to have the aircraft safely brake in a controlled manner that is neither too quickly nor too slowly. In use, these systems allow a pilot to select a selected runway to land and exit the aircraft, and the braking system will decelerate the aircraft hard enough, but just hard enough, to slow the plane to taxi speed by the turnoff that leads to the selected taxiway or terminal. Once the pilot selects the appropriate runway exit during the approach to landing, the system regulates the aircraft's deceleration after touchdown. This enables the aircraft to reach any chosen exit at the correct speed under optimum conditions, no matter what the prevailing conditions are, including poor weather and visibility. A focus of these new systems is that they optimize the braking so that the aircraft gets to the taxiway intersection sooner (i.e., the aircraft does not decelerate too hard too soon, keeping speed up to minimize time spent on the runway) and also prevents overshooting of the intersection, which would then result in a relatively slow taxi to the next available turn off.

One such system is proposed in U.S. Pat. No. 9,102,404 entitled Method For Controlling The Deceleration On The Ground Of A Vehicle, the contents of which are incorporated herein by reference. In order to determine the appropriate braking force needed to precisely decelerate the vehicle, several parameters must be known. One very important consideration is the estimation of a precise distance estimate between vehicle touchdown and exit location/runway overshoot location; furthermore, the distance estimate between the aircraft's current position and the selected exit point would be continuously computed as the aircraft decelerates on the runway. Some navigational systems rely on a branch of spherical mathematics called geodesics to calculate the distances between points on or above the Earth. A common approach is that proposed by Sodano and Robinson in their paper, “Direct And Inverse Solutions Of Geodesics” U.S. Army's Technical Report No. 7. For integration of real-time, braking distance calculations into aircraft that utilize geodesics in the navigation software may require a form of this type of mathematics.

The problem with the use of geodesics to conduct distance calculations is that they require an iterative approach to arrive at a solution, which is taxing on a computational system such as a brake system controller, especially when the computations are required in real-time. In many cases, the distance calculations can overwhelm the system. What is needed is a simplified approach that preserves the necessary accuracy of the braking system runway distance estimates but can reduce the calculations to arithmetic functions rather than iterative functions.

By using a simplified aircraft brake distance estimation, calculations can be performed continuously in real-time that precisely determine and control braking to achieve the selected speed when the aircraft reaches the selected taxiway exit. Additionally, by using this simplified aircraft brake distance estimation, calculations can be used to create a warning of potential runway end excursions and/or initiate braking actions to prevent runway end excursions. These calculations can be used to create a “landing long” warning and aggressively control braking to make up for the shortened available runway distance if an airplane lands too far along the length of the runway. In keeping with this added functionality, these calculations could be used to warn if sufficient runway is not available even prior to touchdown.

SUMMARY OF THE INVENTION

The present invention is a braking system and method utilizing a simplified estimate of a distance between two locations on the earth based on spherical geometry where the distance between the two points is relatively small. A braking system utilizing the aforementioned simplified estimate is more efficient and better equipped to handle rapidly changing estimates for braking needs and variable conditions, making the braking system more robust than prior art systems. In the present invention, geodesics evaluations are replaced with a modified Haversine formula that can include a one-time computation of the cosine of latitude coordinate using, if appropriate, a truncated power series calculation.

These and other features of the present invention will best be understood with reference to the detailed description of the preferred embodiment provided below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 a top view of an aircraft on a landing strip/airport runway;

FIG. 2 is a schematic showing the earth's radius and the distance approximation;

FIG. 3 is a schematic diagram of a system for applying a braking force to a landing gear; and

FIG. 4 is a flow chart illustrating a method of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates a first preferred embodiment and application of the present invention, generally depicting an aircraft 10 landing on a runway having an exit ramp 30. We can identify a location on the runway X_(TD) where the aircraft touches down, and this value can be updated to the aircraft's present position on the runway if necessary. The location on the runway where the aircraft must exit the runway is designated X_(EXIT), where the goal is to decelerate the aircraft to the exit location as quickly and as safely as possible to make room for other landing aircraft or aircraft taking off. Therefore, the goal of the invention is to reduce the time that the aircraft takes in getting from X_(TD) to X_(EXIT) while applying all of the necessary safety regulations and factors. That is, the aircraft must be brought from its landing speed to a selected taxiing speed in a manner that minimizes the residency time of the aircraft on runway 20. X_(END) represents the end of the runway for use in generating pilot warnings for potential runway excursions.

The present invention applies a specific braking force using the aircraft's braking system autobrake functionality. When a pilot preselects a taxiway at which the aircraft will exit the designated runway, the autobrake control manages the deceleration in manner such that the aircraft is moving at a preselected velocity as it reaches the runway exit with the minimal amount of time on the runway, within safety and protocol standards. The invention dynamically determines the brake to exit distance using a modified Haversine formula with a small angle approximation that reduces to an arithmetic calculation.

For any two points on a sphere, the Haversine of the central angle between them is given by

${{hav}\left( \frac{d}{r} \right)} = {{{hav}\left( {\varphi_{2} - \varphi_{1}} \right)} + {{\cos\left( \varphi_{1} \right)}{\cos\left( \varphi_{2} \right)}{{hav}\left( {\lambda_{2} - \lambda_{1}} \right)}}}$

where hav is the Haversine function:

${{hav}(\theta)} = {{\sin^{2}\left( \frac{\theta}{2} \right)} = \frac{1 - {\cos(\theta)}}{2}}$

d is the distance between the two points (along a great circle of the sphere; see spherical distance)

r is the radius of the sphere (see FIG. 2),

φ₁, φ₂: latitude of point 1 and latitude of point 2, in radians

λ₁, λ₂: longitude of point 1 and longitude of point 2, in radians

Solving for d, one can obtain the following formula:

$= {2r\;{\arcsin\left( \sqrt{{\sin^{2}\left( \frac{\varphi_{2} - \varphi_{1}}{2} \right)} + {{\cos\left( \varphi_{1} \right)}{\cos\left( \varphi_{2} \right)}{\sin^{2}\left( \frac{\lambda_{2} - \lambda_{1}}{2} \right)}}} \right)}}$

This represents the distance between two points on a sphere having an radius r at the respective latitude and longitudes. Note that in relation to the size of the earth, for applications where the distances are on a runway of an airport then |φ₂−φ₁|<<1 and |λ₂−λ₁|<<1. Therefore, the preceding equation can be reduced to

$d = {2r{\sin^{- 1}\left( \sqrt{{\frac{1}{4}\left( {\varphi_{2} - \varphi_{1}} \right)^{2}} + {\frac{\cos\;\varphi_{1}\cos\;\varphi_{2}}{4}\left( {\lambda_{2} - \lambda_{1}} \right)^{2}}} \right)}}$

If |φ₂−φ₁|<<1, then φ₂≈φ₁ and cos φ₂≈cos φ₁→cos φ₁ cos φ₂≈cos² φ₁

This leads to

d=2r sin⁻¹√{square root over ((½(φ₂−φ₁)²+(cos φ₁)²(λ₂−λ₁)²)})

Here, the term inside the sin⁻¹ function is much smaller than 1 because (φ₂−φ₁)² and (λ₂−λ₁)² are individually much less than 1, and for any φ₁, 0≤cos² φ₁≤1. Therefore, since for small angles, α: α≈sin α≈sin⁻¹ α, then the equation further reduces to

d=2r(½)√{square root over ((φ₂−φ₁)²+(cos φ₁)²(λ₂−λ₁)²)}

d=r√{square root over ((φ₂−φ₁)²+(cos φ₁)²(λ₂−λ₁)²)}

Since cos² φ₁=½[1+cos 2 φ₁], the equation can also be written as

d=√{square root over ((φ₂−φ₁)²+½[1+cos 2 φ₁](λ₂−λ₁)²)}

The cosine term in this equation can be evaluated using a look-up table of values stored in a the memory of the braking system's processor, or other known approximations for the trigonometric function. Since this term is a constant throughout the braking run, it only has to be computed or looked up once at or before the beginning of the braking run.

Also, the cosine function can be written as a power series:

cos φ₁=1−(½!)[φ₁ ²]+(¼!)[φ₁ ⁴]- . . .

Thus, another method for approximating the cosine term in the distance calculation would be to compute it to sufficient accuracy using an appropriate number of terms of this power series. Using a truncated power series approximation for the cosine term (done only once per braking run), the simplified distance equation is therefore reduced to a number of arithmetic calculations that can easily be handled dynamically by a brake control system processor.

The aircraft's navigation system provides longitude and latitude coordinates, φ_(s) and λ_(s), as necessary to complete the calculations for the distance estimation. With the simplification described above, there are no iterative computations needed and the distance can be readily determined quickly and without undue computational processing.

To implement an autobraking system that utilizes the foregoing approximations, FIG. 3 illustrates a schematic diagram of a processor 50 of an aircraft's braking system that is equipped with a distance approximation module using the Haversine approximation. The aircraft's navigation system 35 provides geodetic data to the processor 50, which converts the data to a position of the aircraft on the earth's spherical surface. Using known positions of the runway exits, the distance upon touchdown to the runway exit can be determined using the power series approximation of the cosine of θ. Once the distance is obtained to the runway exit, the processor 50 calculates the necessary deceleration and sends the appropriate commands to a braking actuator 60 to apply a braking force to the aircraft wheels. The processor can also receive data from wheel speed sensor 70, and environmental conditions such as runway surface condition, wind speed, temperature, maximum velocity, etc. from flight deck input 80. The processor 50 applies all of the inputs and conditions, and sends the braking commands to brake actuator 60 for decelerating the aircraft according to the minimum residency protocol.

FIG. 4 illustrates a flow control diagram for a method of braking the aircraft according to the present invention. In step 100, the aircraft's navigation system provides a current position of the aircraft using geodetic data. In step 110, the braking system determines a distance from its current location to a predetermined runway exit from the geodetic data using a Haversine formula. Once the distance is obtained, the braking system in step 120 generates selected kinematics for the aircraft to travel from touchdown to a runway exit that minimizes the residency time of the aircraft on the runway. In step 130, the velocity profile is used to generate aircraft wheel braking commands using the distance estimation and current speed and position of the aircraft. The braking commands are communicated in step 140 to the brake actuator, which in turn applies a braking force to the aircraft wheels consistent with the velocity profile in step 150. Note that other inputs may be preferably incorporated into the processor for determining the velocity profile, including current weather conditions, runway surface conditions, weight of the aircraft, etc.

While the inventor has described some of the preferred embodiments of the present invention, the invention should not be construed so as to be limited to the embodiments depicted and described herein. Rather, the scope of the invention is governed by the appended claims, without limitation to any specific embodiment or illustration. 

We claim:
 1. A braking system for reducing a speed of an aircraft on a runway, comprising: a processor including a memory for storing a program to calculate braking parameters; a braking actuator responsive to commands from the processor; and an aircraft navigation system adapted to provide current aircraft position data and position data for a selected location on said runway to the processor; wherein the processor uses a Haversine formula small angle simplification to estimate the distance between a current aircraft position and the selected location on said runway; and wherein the processor commands the braking actuator to reduce the speed of the aircraft based on the estimate of the distance between the current aircraft position and the selected location on said runway.
 2. The braking system for reducing a speed of an aircraft of claim 1, wherein the braking system uses a preselected exit position to determine the braking actuator's reduction of the aircraft speed to minimize a residency time on a runway.
 3. The braking system of claim 1, wherein the estimate of the distance between the current aircraft position and the selected location on said runway computes the cosine of the latitude angle using a truncated power series.
 4. The braking system of claim 1, wherein the estimate of the distance between the current aircraft position and the selected location on said runway computes the cosine of the latitude angle using a lookup table.
 5. A method for adjusting instantaneous deceleration of an aircraft to minimize an occupancy of an aircraft on a runway, comprising: obtaining a current aircraft position after touchdown using geodetic data; generating a deceleration profile for the aircraft to travel from touchdown to a selected location on said runway with a selected exit taxi speed; determining a distance from a current aircraft location to a selected location on said runway from the geodetic data using a Haversine formula small angle derivation for a distance estimation; generating a deceleration profile using the distance estimation and current aircraft speed and current aircraft position; and commanding a brake actuator to decelerate the aircraft based on the generated deceleration profile.
 6. The method of claim 5, wherein the estimation of the distance between the current aircraft position and the selected location on said runway computes the cosine of a latitude angle using a truncated power series.
 7. The method of claim 5, wherein the estimation of the distance between the current aircraft position and the selected location on said runway computes the cosine of a latitude angle using a lookup table.
 8. A braking system for reducing a speed of an aircraft on a runway, comprising: a processor including a memory for storing a program to calculate braking parameters; a braking actuator responsive to commands from the processor; and an aircraft navigation system adapted to provide current aircraft position data and position data for a selected location on said runway to the processor; wherein the processor uses a Haversine formula small angle simplification to estimate the distance between a current aircraft position and the selected location on said runway; and wherein the processor generates a deceleration profile and issues a warning signal if there is potential for the aircraft to overrun the selected location based on the deceleration profile.
 9. The braking system of claim 8, wherein the deceleration profile and warning signal are generated prior to and after aircraft touchdown on the runway.
 10. The braking system of claim 8, wherein the estimation of the distance between the current aircraft position and the selected position on the runway computes the cosine of the latitude angle using a truncated power series.
 11. The braking system of claim 8, wherein the estimation of the distance between the current aircraft position and the selected position on the runway computes the cosine of the latitude angle using a lookup table.
 12. A method for adjusting instantaneous deceleration of an aircraft to minimize an occupancy of an aircraft on a runway, comprising: obtaining a current aircraft position after touchdown using geodetic data; generating a deceleration profile for the aircraft to travel from touchdown to a selected location on said runway with a selected exit taxi speed; determining a distance from a current aircraft location to a selected location on said runway from the geodetic data using a Haversine formula small angle derivation for a distance estimation; generating a deceleration profile using the distance estimation and current aircraft speed and current aircraft position; and generating a deceleration profile and issuing a warning signal to a cockpit of the aircraft if there is potential for the aircraft to overrun the selected location on the runway.
 13. The method of claim 12, wherein the deceleration profile and warning signal are generated prior to and after aircraft touchdown on the runway.
 14. The method of claim 12, wherein the estimation of the distance between the current aircraft position and the selected location on the runway computes the cosine of the latitude angle using a truncated power series.
 15. The method of claim 12, wherein the estimation of the distance between the current aircraft position and the selected location on the runway computes the cosine of the latitude angle using a lookup table.
 16. A braking system for reducing a speed of an aircraft, comprising: a processor including a memory for storing a program to calculate braking parameters; a braking actuator responsive to commands from the processor; and an aircraft navigation system adapted to provide current aircraft position data and position data for a selected location on said runway to the processor; wherein the processor uses a Haversine formula small angle simplification to estimate the distance between a current aircraft position and the selected location on said runway; and wherein the processor commands the braking actuator to initiate maximum braking force when the processor determines that the aircraft will overrun the selected location on said runway.
 17. The braking system of claim 16, wherein the estimation of the distance between the current aircraft position and the selected location on said runway computes the cosine of the latitude angle using a truncated power series.
 18. The braking system of claim 16, wherein the estimation of the distance between the current aircraft position and the selected location on said runway computes the cosine of the latitude angle using a lookup table.
 19. The braking system of claim 16, further including the step of generating a warning signal when the processor determines that the aircraft will overrun the selected location on said runway.
 20. A method for reducing a speed of an aircraft, comprising: providing a processor including memory for storing a program for calculating braking parameters; providing a braking actuator responsive to commands from the processor; incorporating an aircraft navigation system that provides current aircraft position data and position data for a selected location on a runway to the processor; using a Haversine formula small angle simplification to estimate a distance between the current aircraft position and the selected location on the runway; and commanding the braking actuator to initiate maximum a braking force when the processor determines that the aircraft will overrun the selected location on the runway.
 21. The method of claim 20, wherein the estimation of the distance between the current aircraft position and the selected location on the runway is computed using a truncated power series for the cosine of the latitude angle.
 22. The method of claim 20, wherein the estimation of the distance between the current aircraft position and the selected location on the runway is computed using a look-up table for the cosine of the latitude angle.
 23. The method of claim 20, further including a step of generating a warning signal when the processor determines that the aircraft will overrun the selected location on the runway. 